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Monte Carlo studies of the ordering of the one-dimensional Heisenberg spin glass with long-range power-law interactions

The nature of the ordering of the one-dimensional Heisenberg spin-glass model with a long-range power-law interaction is studied by extensive Monte Carlo simulations, with particular attention to the issue of the spin-chirality decoupling/coupling. Large system sizes up to $L=4096$ are studied. With varying the exponent $σ$ describing the power-law interaction, we observe three distinct types of ordering regimes. For smaller $σ$, the spin and the chirality order at a common finite temperature with a common correlation-length exponent, exhibiting the standard spin-chirality coupling behavior. For intermediate $σ$, the chirality orders at a temperature higher than the spin, exhibiting the spin-chirality decoupling behavior. For larger $σ$, both the spin and the chirality order at zero temperature. We construct a phase diagram in the $σ$ versus the temperature plane, and discuss implications of the results. Critical properties associated with both the chiral-glass and the spin-glass transitions are also determined.